MinT - Best Known (73, 216, s)-Nets in Base 4

Best Known (73, 216, s)-Nets in Base 4

(73, 216, 104)-Net over F₄ — Constructive and digital

Digital (73, 216, 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]

(73, 216, 112)-Net over F₄ — Digital

Digital (73, 216, 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]

(73, 216, 548)-Net in Base 4 — Upper bound on s

There is no (73, 216, 549)-net in base 4, because

1 times m-reduction [i] would yield (73, 215, 549)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3028 564982 301768 519950 461759 865261 930321 724425 436103 906821 711867 637650 375284 411973 561632 244862 841829 788290 683288 117478 463997 518080 > 4²¹⁵ [i]