MinT - Best Known (144−71, 144, s)-Nets in Base 4

Best Known (144−71, 144, s)-Nets in Base 4

(144−71, 144, 104)-Net over F₄ — Constructive and digital

Digital (73, 144, 104)-net over F₄, using

net from sequence [i] based on digital (73, 103)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
  - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(144−71, 144, 113)-Net over F₄ — Digital

Digital (73, 144, 113)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−71, 144, 1308)-Net in Base 4 — Upper bound on s

There is no (73, 144, 1309)-net in base 4, because

1 times m-reduction [i] would yield (73, 143, 1309)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127 214839 393762 534221 742569 091111 454399 372700 391469 991859 740068 706817 518359 221227 457120 > 4¹⁴³ [i]