MinT - Best Known (220−147, 220, s)-Nets in Base 4

Best Known (220−147, 220, s)-Nets in Base 4

(220−147, 220, 104)-Net over F₄ — Constructive and digital

Digital (73, 220, 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]

(220−147, 220, 112)-Net over F₄ — Digital

Digital (73, 220, 112)-net over F₄, using

net from sequence [i] based on digital (73, 111)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
  - Drinfeld modules of rank 1 [i]

(220−147, 220, 539)-Net in Base 4 — Upper bound on s

There is no (73, 220, 540)-net in base 4, because

1 times m-reduction [i] would yield (73, 219, 540)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 768148 867308 328984 348686 632704 980967 874504 083392 727535 803347 870767 453945 233984 243682 396339 014963 791260 440458 639840 036741 504716 612200 > 4²¹⁹ [i]