MinT - Best Known (187−75, 187, s)-Nets in Base 4

Best Known (187−75, 187, s)-Nets in Base 4

(187−75, 187, 130)-Net over F₄ — Constructive and digital

Digital (112, 187, 130)-net over F₄, using

t-expansion [i] based on digital (105, 187, 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]

(187−75, 187, 273)-Net over F₄ — Digital

Digital (112, 187, 273)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−75, 187, 5162)-Net in Base 4 — Upper bound on s

There is no (112, 187, 5163)-net in base 4, because

1 times m-reduction [i] would yield (112, 186, 5163)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9683 876423 415808 218553 914221 826617 524287 952158 845624 513251 262982 335021 839440 806934 966511 827130 769240 430193 922188 > 4¹⁸⁶ [i]