MinT - Best Known (248−133, 248, s)-Nets in Base 4

Best Known (248−133, 248, s)-Nets in Base 4

(248−133, 248, 130)-Net over F₄ — Constructive and digital

Digital (115, 248, 130)-net over F₄, using

t-expansion [i] based on digital (105, 248, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(248−133, 248, 168)-Net over F₄ — Digital

Digital (115, 248, 168)-net over F₄, using

net from sequence [i] based on digital (115, 167)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(248−133, 248, 1463)-Net in Base 4 — Upper bound on s

There is no (115, 248, 1464)-net in base 4, because

1 times m-reduction [i] would yield (115, 247, 1464)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51719 834186 901699 360457 425359 496076 043610 390398 636021 286177 813602 474567 281213 700707 450601 330666 958783 510946 482540 913198 435834 749796 580840 151770 349910 > 4²⁴⁷ [i]