MinT - Best Known (242−163, 242, s)-Nets in Base 4

Best Known (242−163, 242, s)-Nets in Base 4

(242−163, 242, 104)-Net over F₄ — Constructive and digital

Digital (79, 242, 104)-net over F₄, using

t-expansion [i] based on 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]

(242−163, 242, 112)-Net over F₄ — Digital

Digital (79, 242, 112)-net over F₄, using

t-expansion [i] based on 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]

(242−163, 242, 573)-Net in Base 4 — Upper bound on s

There is no (79, 242, 574)-net in base 4, because

1 times m-reduction [i] would yield (79, 241, 574)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 568766 618880 996269 608098 741613 923089 192174 528817 833150 455838 170258 872880 975151 150906 396843 604254 666246 598957 617189 748476 745252 453533 687791 077880 > 4²⁴¹ [i]