MinT - Best Known (110, 177, s)-Nets in Base 4

Best Known (110, 177, s)-Nets in Base 4

(110, 177, 130)-Net over F₄ — Constructive and digital

Digital (110, 177, 130)-net over F₄, using

t-expansion [i] based on digital (105, 177, 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]

(110, 177, 317)-Net over F₄ — Digital

Digital (110, 177, 317)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 177, 7105)-Net in Base 4 — Upper bound on s

There is no (110, 177, 7106)-net in base 4, because

1 times m-reduction [i] would yield (110, 176, 7106)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9209 168087 219885 807958 344430 115624 896216 131818 368102 819420 891034 917348 989627 947152 780988 393408 652581 308838 > 4¹⁷⁶ [i]