MinT - Best Known (243−150, 243, s)-Nets in Base 4

Best Known (243−150, 243, s)-Nets in Base 4

(243−150, 243, 104)-Net over F₄ — Constructive and digital

Digital (93, 243, 104)-net over F₄, using

t-expansion [i] based on digital (73, 243, 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]

(243−150, 243, 144)-Net over F₄ — Digital

Digital (93, 243, 144)-net over F₄, using

t-expansion [i] based on digital (91, 243, 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]

(243−150, 243, 795)-Net in Base 4 — Upper bound on s

There is no (93, 243, 796)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 217 934868 842545 268286 792023 578158 335305 419083 024684 897044 679128 382107 795548 989680 967032 418652 172269 476876 433575 527295 867741 688762 723265 894438 840708 > 4²⁴³ [i]