MinT - Best Known (110, 243, s)-Nets in Base 4

Best Known (110, 243, s)-Nets in Base 4

(110, 243, 130)-Net over F₄ — Constructive and digital

Digital (110, 243, 130)-net over F₄, using

t-expansion [i] based on digital (105, 243, 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, 243, 165)-Net over F₄ — Digital

Digital (110, 243, 165)-net over F₄, using

t-expansion [i] based on digital (109, 243, 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, 243, 1312)-Net in Base 4 — Upper bound on s

There is no (110, 243, 1313)-net in base 4, because

1 times m-reduction [i] would yield (110, 242, 1313)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51 084603 780944 211882 547181 284800 309815 818798 065737 615477 879135 150680 166897 256840 701782 552874 951051 982503 350477 614489 326536 682461 435555 596203 973760 > 4²⁴² [i]