MinT - Best Known (218−103, 218, s)-Nets in Base 4

Best Known (218−103, 218, s)-Nets in Base 4

(218−103, 218, 130)-Net over F₄ — Constructive and digital

Digital (115, 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]

(218−103, 218, 185)-Net over F₄ — Digital

Digital (115, 218, 185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−103, 218, 2370)-Net in Base 4 — Upper bound on s

There is no (115, 218, 2371)-net in base 4, because

1 times m-reduction [i] would yield (115, 217, 2371)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44711 387437 266946 244412 828632 316163 909098 578062 341211 226290 833493 206363 125247 233222 507278 530841 279401 990290 579821 774628 542258 970704 > 4²¹⁷ [i]