MinT - Best Known (242−169, 242, s)-Nets in Base 4

Best Known (242−169, 242, s)-Nets in Base 4

(242−169, 242, 104)-Net over F₄ — Constructive and digital

Digital (73, 242, 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]

(242−169, 242, 112)-Net over F₄ — Digital

Digital (73, 242, 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]

(242−169, 242, 504)-Net in Base 4 — Upper bound on s

There is no (73, 242, 505)-net in base 4, because

1 times m-reduction [i] would yield (73, 241, 505)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 967881 057505 612190 473719 239331 556659 940979 207310 876836 560788 831558 566515 280784 430104 572288 128323 896449 082444 848227 951228 213296 454044 895914 233086 > 4²⁴¹ [i]