MinT - Best Known (97−49, 97, s)-Nets in Base 32

Best Known (97−49, 97, s)-Nets in Base 32

(97−49, 97, 240)-Net over F₃₂ — Constructive and digital

Digital (48, 97, 240)-net over F₃₂, using

3 times m-reduction [i] based on digital (48, 100, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 37, 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]
  2. digital (11, 63, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(97−49, 97, 513)-Net in Base 32 — Constructive

(48, 97, 513)-net in base 32, using

t-expansion [i] based on (46, 97, 513)-net in base 32, using
- 11 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]

(97−49, 97, 682)-Net over F₃₂ — Digital

Digital (48, 97, 682)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−49, 97, 331577)-Net in Base 32 — Upper bound on s

There is no (48, 97, 331578)-net in base 32, because

1 times m-reduction [i] would yield (48, 96, 331578)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 121891 400418 065780 584483 531431 264815 690005 728791 360690 791117 149970 098745 517848 471333 754072 417597 615134 093137 306158 323954 347635 922948 790666 880819 > 32⁹⁶ [i]