MinT - Best Known (123, 123+117, s)-Nets in Base 4

Best Known (123, 123+117, s)-Nets in Base 4

(123, 123+117, 130)-Net over F₄ — Constructive and digital

Digital (123, 240, 130)-net over F₄, using

t-expansion [i] based on digital (105, 240, 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]

(123, 123+117, 183)-Net over F₄ — Digital

Digital (123, 240, 183)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+117, 2217)-Net in Base 4 — Upper bound on s

There is no (123, 240, 2218)-net in base 4, because

1 times m-reduction [i] would yield (123, 239, 2218)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 795863 127472 556043 927702 433130 717469 498970 329990 003297 662891 629331 937451 674935 330354 382974 110587 288471 194472 795340 872497 789927 541839 267218 259200 > 4²³⁹ [i]