MinT - Best Known (103−56, 103, s)-Nets in Base 32

Best Known (103−56, 103, s)-Nets in Base 32

(103−56, 103, 218)-Net over F₃₂ — Constructive and digital

Digital (47, 103, 218)-net over F₃₂, using

2 times m-reduction [i] based on digital (47, 105, 218)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 36, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]
  2. digital (11, 69, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(103−56, 103, 449)-Net over F₃₂ — Digital

Digital (47, 103, 449)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−56, 103, 513)-Net in Base 32 — Constructive

(47, 103, 513)-net in base 32, using

t-expansion [i] based on (46, 103, 513)-net in base 32, using
- 5 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
  - base change [i] based on digital (28, 90, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(103−56, 103, 125428)-Net in Base 32 — Upper bound on s

There is no (47, 103, 125429)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107281 724600 513403 181539 647872 815348 731141 951126 211029 940618 013834 627104 354672 007587 517391 872248 344304 053853 629554 871651 416112 022207 820529 830333 132619 751852 > 32¹⁰³ [i]