MinT - Best Known (196−91, 196, s)-Nets in Base 4

Best Known (196−91, 196, s)-Nets in Base 4

(196−91, 196, 130)-Net over F₄ — Constructive and digital

Digital (105, 196, 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]

(196−91, 196, 178)-Net over F₄ — Digital

Digital (105, 196, 178)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−91, 196, 2350)-Net in Base 4 — Upper bound on s

There is no (105, 196, 2351)-net in base 4, because

1 times m-reduction [i] would yield (105, 195, 2351)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2525 845519 647644 434549 747332 695145 114213 586674 739224 466065 028101 615385 922220 616198 291568 294970 692079 258930 366875 289526 > 4¹⁹⁵ [i]