MinT - Best Known (73, 199, s)-Nets in Base 4

Best Known (73, 199, s)-Nets in Base 4

(73, 199, 104)-Net over F₄ — Constructive and digital

Digital (73, 199, 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, 199, 112)-Net over F₄ — Digital

Digital (73, 199, 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, 199, 595)-Net in Base 4 — Upper bound on s

There is no (73, 199, 596)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 669607 249502 205677 390668 430190 312816 977127 975223 004391 726301 750406 332656 707710 827368 268838 238360 521469 929982 784820 526320 > 4¹⁹⁹ [i]