MinT - Best Known (22, 98, s)-Nets in Base 32

Best Known (22, 98, s)-Nets in Base 32

(22, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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]

(22, 98, 128)-Net in Base 32 — Constructive

(22, 98, 128)-net in base 32, using

4 times m-reduction [i] based on (22, 102, 128)-net in base 32, using
- base change [i] based on digital (5, 85, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(22, 98, 185)-Net over F₃₂ — Digital

Digital (22, 98, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 98, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(22, 98, 3671)-Net in Base 32 — Upper bound on s

There is no (22, 98, 3672)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3219 893175 379446 876662 088052 632031 521365 122168 055199 522208 850121 049470 036342 652373 227956 638134 689001 358275 903645 069862 875920 662590 763818 358416 123670 > 32⁹⁸ [i]