MinT - Best Known (75, 75+69, s)-Nets in Base 9

Best Known (75, 75+69, s)-Nets in Base 9

(75, 75+69, 232)-Net over F₉ — Constructive and digital

Digital (75, 144, 232)-net over F₉, using

2 times m-reduction [i] based on digital (75, 146, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 73, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(75, 75+69, 322)-Net over F₉ — Digital

Digital (75, 144, 322)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+69, 17430)-Net in Base 9 — Upper bound on s

There is no (75, 144, 17431)-net in base 9, because

1 times m-reduction [i] would yield (75, 143, 17431)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28669 110633 858687 082787 808562 492516 417497 731630 547754 858513 185500 068583 641813 351690 978906 725883 128961 346485 507306 255889 795192 997322 362225 > 9¹⁴³ [i]