MinT - Best Known (218−97, 218, s)-Nets in Base 4

Best Known (218−97, 218, s)-Nets in Base 4

(218−97, 218, 130)-Net over F₄ — Constructive and digital

Digital (121, 218, 130)-net over F₄, using

t-expansion [i] based on digital (105, 218, 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]

(218−97, 218, 224)-Net over F₄ — Digital

Digital (121, 218, 224)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−97, 218, 3252)-Net in Base 4 — Upper bound on s

There is no (121, 218, 3253)-net in base 4, because

1 times m-reduction [i] would yield (121, 217, 3253)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44463 923205 624437 890254 736024 940012 747848 328524 326457 610508 981475 098366 701646 665979 619751 684966 296709 949095 032402 109297 472999 629545 > 4²¹⁷ [i]