MinT - Best Known (248−160, 248, s)-Nets in Base 4

Best Known (248−160, 248, s)-Nets in Base 4

(248−160, 248, 104)-Net over F₄ — Constructive and digital

Digital (88, 248, 104)-net over F₄, using

t-expansion [i] based on digital (73, 248, 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]

(248−160, 248, 129)-Net over F₄ — Digital

Digital (88, 248, 129)-net over F₄, using

t-expansion [i] based on digital (81, 248, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(248−160, 248, 685)-Net in Base 4 — Upper bound on s

There is no (88, 248, 686)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209727 026481 100871 340887 664660 100684 247972 491086 316630 625648 191074 264307 161759 420851 095229 214877 997732 288618 660092 809443 617232 390857 364983 492662 552220 > 4²⁴⁸ [i]