MinT - Best Known (244−171, 244, s)-Nets in Base 4

Best Known (244−171, 244, s)-Nets in Base 4

(244−171, 244, 104)-Net over F₄ — Constructive and digital

Digital (73, 244, 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]

(244−171, 244, 112)-Net over F₄ — Digital

Digital (73, 244, 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]

(244−171, 244, 501)-Net in Base 4 — Upper bound on s

There is no (73, 244, 502)-net in base 4, because

1 times m-reduction [i] would yield (73, 243, 502)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 201 492179 598773 294849 289156 032423 932535 378218 263261 300117 603385 775374 433004 447418 310738 804447 362729 988108 266377 047749 215262 772614 151247 613669 239709 > 4²⁴³ [i]