MinT - Best Known (196−83, 196, s)-Nets in Base 4

Best Known (196−83, 196, s)-Nets in Base 4

(196−83, 196, 130)-Net over F₄ — Constructive and digital

Digital (113, 196, 130)-net over F₄, using

t-expansion [i] based on 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]

(196−83, 196, 239)-Net over F₄ — Digital

Digital (113, 196, 239)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−83, 196, 3895)-Net in Base 4 — Upper bound on s

There is no (113, 196, 3896)-net in base 4, because

1 times m-reduction [i] would yield (113, 195, 3896)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2544 650150 130824 089681 253102 227179 119603 153745 499316 638845 251171 231532 663028 507572 526491 899167 851808 969325 491921 523806 > 4¹⁹⁵ [i]