MinT - Best Known (208−89, 208, s)-Nets in Base 4

Best Known (208−89, 208, s)-Nets in Base 4

(208−89, 208, 130)-Net over F₄ — Constructive and digital

Digital (119, 208, 130)-net over F₄, using

t-expansion [i] based on digital (105, 208, 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]

(208−89, 208, 244)-Net over F₄ — Digital

Digital (119, 208, 244)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−89, 208, 3874)-Net in Base 4 — Upper bound on s

There is no (119, 208, 3875)-net in base 4, because

1 times m-reduction [i] would yield (119, 207, 3875)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42617 819012 485157 561554 312332 154611 228281 999036 650926 907941 065840 010060 080466 614394 522301 873161 403194 090989 625752 995832 574016 > 4²⁰⁷ [i]