MinT - Best Known (115, 115+85, s)-Nets in Base 4

Best Known (115, 115+85, s)-Nets in Base 4

(115, 115+85, 130)-Net over F₄ — Constructive and digital

Digital (115, 200, 130)-net over F₄, using

t-expansion [i] based on digital (105, 200, 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]

(115, 115+85, 241)-Net over F₄ — Digital

Digital (115, 200, 241)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+85, 3885)-Net in Base 4 — Upper bound on s

There is no (115, 200, 3886)-net in base 4, because

1 times m-reduction [i] would yield (115, 199, 3886)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 647465 989071 322226 552187 466928 401186 572382 620719 589543 126934 481087 608876 123028 487029 074974 334330 143853 313107 755036 266470 > 4¹⁹⁹ [i]