MinT - Best Known (218−93, 218, s)-Nets in Base 4

Best Known (218−93, 218, s)-Nets in Base 4

(218−93, 218, 130)-Net over F₄ — Constructive and digital

Digital (125, 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]

(218−93, 218, 256)-Net over F₄ — Digital

Digital (125, 218, 256)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−93, 218, 4114)-Net in Base 4 — Upper bound on s

There is no (125, 218, 4115)-net in base 4, because

1 times m-reduction [i] would yield (125, 217, 4115)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44691 326690 950959 261921 278981 328628 245433 555005 976358 725186 650222 074077 613657 506442 318339 629990 484470 142177 766464 963545 298512 539136 > 4²¹⁷ [i]