MinT - Best Known (185−79, 185, s)-Nets in Base 4

Best Known (185−79, 185, s)-Nets in Base 4

(185−79, 185, 130)-Net over F₄ — Constructive and digital

Digital (106, 185, 130)-net over F₄, using

t-expansion [i] based on digital (105, 185, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(185−79, 185, 221)-Net over F₄ — Digital

Digital (106, 185, 221)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−79, 185, 3522)-Net in Base 4 — Upper bound on s

There is no (106, 185, 3523)-net in base 4, because

1 times m-reduction [i] would yield (106, 184, 3523)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 603 065812 223069 599254 567372 142823 628822 999216 186867 446879 917129 893135 693531 241362 923010 657200 465113 212567 612544 > 4¹⁸⁴ [i]