MinT - Best Known (136−66, 136, s)-Nets in Base 9

Best Known (136−66, 136, s)-Nets in Base 9

(136−66, 136, 232)-Net over F₉ — Constructive and digital

Digital (70, 136, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 68, 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]

(136−66, 136, 290)-Net over F₉ — Digital

Digital (70, 136, 290)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−66, 136, 14069)-Net in Base 9 — Upper bound on s

There is no (70, 136, 14070)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 5990 528967 754644 959605 724143 301913 744441 116541 097936 138842 073030 096497 226591 022030 451215 419441 636806 347174 834066 150927 339797 471665 > 9¹³⁶ [i]