MinT - Best Known (218−105, 218, s)-Nets in Base 4

Best Known (218−105, 218, s)-Nets in Base 4

(218−105, 218, 130)-Net over F₄ — Constructive and digital

Digital (113, 218, 130)-net over F₄, using

t-expansion [i] based on digital (105, 218, 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]

(218−105, 218, 174)-Net over F₄ — Digital

Digital (113, 218, 174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−105, 218, 2151)-Net in Base 4 — Upper bound on s

There is no (113, 218, 2152)-net in base 4, because

1 times m-reduction [i] would yield (113, 217, 2152)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45007 011606 202065 265733 853286 444096 895569 249609 254405 128099 081909 923721 567012 249235 392195 097503 119419 461571 302676 074734 807172 200900 > 4²¹⁷ [i]