MinT - Best Known (214−99, 214, s)-Nets in Base 4

Best Known (214−99, 214, s)-Nets in Base 4

(214−99, 214, 130)-Net over F₄ — Constructive and digital

Digital (115, 214, 130)-net over F₄, using

t-expansion [i] based on digital (105, 214, 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]

(214−99, 214, 195)-Net over F₄ — Digital

Digital (115, 214, 195)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−99, 214, 2598)-Net in Base 4 — Upper bound on s

There is no (115, 214, 2599)-net in base 4, because

1 times m-reduction [i] would yield (115, 213, 2599)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 176 265639 745404 037807 887207 652126 804421 923375 512129 627500 064472 204490 257824 948172 451985 176298 843067 171411 508518 895941 372943 749312 > 4²¹³ [i]