MinT - Best Known (198−83, 198, s)-Nets in Base 4

Best Known (198−83, 198, s)-Nets in Base 4

(198−83, 198, 130)-Net over F₄ — Constructive and digital

Digital (115, 198, 130)-net over F₄, using

t-expansion [i] based on digital (105, 198, 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]

(198−83, 198, 249)-Net over F₄ — Digital

Digital (115, 198, 249)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−83, 198, 4169)-Net in Base 4 — Upper bound on s

There is no (115, 198, 4170)-net in base 4, because

1 times m-reduction [i] would yield (115, 197, 4170)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40352 060965 093610 082783 140106 174348 281278 762850 255362 863131 810323 721851 446403 048072 702117 138604 174142 059735 928324 090754 > 4¹⁹⁷ [i]