MinT - Best Known (98−53, 98, s)-Nets in Base 32

Best Known (98−53, 98, s)-Nets in Base 32

(98−53, 98, 218)-Net over F₃₂ — Constructive and digital

Digital (45, 98, 218)-net over F₃₂, using

1 times m-reduction [i] based on digital (45, 99, 218)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 34, 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, 65, 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]

(98−53, 98, 446)-Net over F₃₂ — Digital

Digital (45, 98, 446)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−53, 98, 513)-Net in Base 32 — Constructive

(45, 98, 513)-net in base 32, using

4 times m-reduction [i] based on (45, 102, 513)-net in base 32, using
- base change [i] based on digital (28, 85, 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]

(98−53, 98, 140364)-Net in Base 32 — Upper bound on s

There is no (45, 98, 140365)-net in base 32, because

1 times m-reduction [i] would yield (45, 97, 140365)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 99 905075 330312 639644 853791 165343 362231 642914 299944 234679 155331 151025 183015 235083 221556 961488 159105 661150 404788 271674 748824 804120 990143 800990 658056 > 32⁹⁷ [i]