MinT - Best Known (136−65, 136, s)-Nets in Base 4

Best Known (136−65, 136, s)-Nets in Base 4

(136−65, 136, 76)-Net over F₄ — Constructive and digital

Digital (71, 136, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 68, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(136−65, 136, 119)-Net over F₄ — Digital

Digital (71, 136, 119)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−65, 136, 1452)-Net in Base 4 — Upper bound on s

There is no (71, 136, 1453)-net in base 4, because

1 times m-reduction [i] would yield (71, 135, 1453)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1934 640232 547456 417489 702688 700965 271621 651980 759885 144172 954481 438956 784784 148201 > 4¹³⁵ [i]