MinT - Best Known (91, 242, s)-Nets in Base 4

Best Known (91, 242, s)-Nets in Base 4

(91, 242, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(91, 242, 144)-Net over F₄ — Digital

Digital (91, 242, 144)-net over F₄, using

net from sequence [i] based on digital (91, 143)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]

(91, 242, 764)-Net in Base 4 — Upper bound on s

There is no (91, 242, 765)-net in base 4, because

1 times m-reduction [i] would yield (91, 241, 765)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 645250 359298 013939 531228 968863 952796 296119 373275 412479 881938 855700 817442 619367 266027 315757 703423 713814 814172 064642 137127 276522 496939 706488 362164 > 4²⁴¹ [i]