MinT - Best Known (72, 72+67, s)-Nets in Base 9

Best Known (72, 72+67, s)-Nets in Base 9

(72, 72+67, 232)-Net over F₉ — Constructive and digital

Digital (72, 139, 232)-net over F₉, using

1 times m-reduction [i] based on digital (72, 140, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 70, 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]

(72, 72+67, 304)-Net over F₉ — Digital

Digital (72, 139, 304)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+67, 16076)-Net in Base 9 — Upper bound on s

There is no (72, 139, 16077)-net in base 9, because

1 times m-reduction [i] would yield (72, 138, 16077)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 485256 898508 899380 155631 226716 024834 613616 965752 246054 790789 487089 394559 946464 548743 595518 199202 153803 711280 998476 448390 513187 131241 > 9¹³⁸ [i]