MinT - Best Known (66, 127, s)-Nets in Base 9

Best Known (66, 127, s)-Nets in Base 9

(66, 127, 232)-Net over F₉ — Constructive and digital

Digital (66, 127, 232)-net over F₉, using

1 times m-reduction [i] based on digital (66, 128, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 64, 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]

(66, 127, 286)-Net over F₉ — Digital

Digital (66, 127, 286)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 127, 15310)-Net in Base 9 — Upper bound on s

There is no (66, 127, 15311)-net in base 9, because

1 times m-reduction [i] would yield (66, 126, 15311)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 716569 059870 715628 591078 411151 878548 179148 454614 668718 507966 133149 862150 805685 397125 532355 580570 457234 829173 136257 983505 > 9¹²⁶ [i]