MinT - Best Known (254−153, 254, s)-Nets in Base 4

Best Known (254−153, 254, s)-Nets in Base 4

(254−153, 254, 104)-Net over F₄ — Constructive and digital

Digital (101, 254, 104)-net over F₄, using

t-expansion [i] based on digital (73, 254, 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]

(254−153, 254, 144)-Net over F₄ — Digital

Digital (101, 254, 144)-net over F₄, using

t-expansion [i] based on digital (91, 254, 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]

(254−153, 254, 918)-Net in Base 4 — Upper bound on s

There is no (101, 254, 919)-net in base 4, because

1 times m-reduction [i] would yield (101, 253, 919)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214 117453 014607 536749 073648 984294 369563 022841 770240 946081 306976 377835 995825 223890 168357 055738 336827 343656 772392 151047 462641 304320 377307 700911 798590 607964 > 4²⁵³ [i]