MinT - Best Known (114, 114+87, s)-Nets in Base 4

Best Known (114, 114+87, s)-Nets in Base 4

(114, 114+87, 130)-Net over F₄ — Constructive and digital

Digital (114, 201, 130)-net over F₄, using

t-expansion [i] based on digital (105, 201, 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]

(114, 114+87, 228)-Net over F₄ — Digital

Digital (114, 201, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+87, 3518)-Net in Base 4 — Upper bound on s

There is no (114, 201, 3519)-net in base 4, because

1 times m-reduction [i] would yield (114, 200, 3519)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 611948 285027 535932 789620 122955 620926 870539 702662 389070 261477 264298 560141 542148 048765 628904 889985 542672 199461 745610 267456 > 4²⁰⁰ [i]