MinT - Best Known (110, 249, s)-Nets in Base 4

Best Known (110, 249, s)-Nets in Base 4

(110, 249, 130)-Net over F₄ — Constructive and digital

Digital (110, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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]

(110, 249, 165)-Net over F₄ — Digital

Digital (110, 249, 165)-net over F₄, using

t-expansion [i] based on digital (109, 249, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(110, 249, 1233)-Net in Base 4 — Upper bound on s

There is no (110, 249, 1234)-net in base 4, because

1 times m-reduction [i] would yield (110, 248, 1234)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209003 030766 576509 018440 360482 735733 043163 651808 643561 041964 724701 163564 846525 009792 204477 232755 806229 379050 632705 119494 674764 522318 242756 398751 197692 > 4²⁴⁸ [i]