MinT - Best Known (222−112, 222, s)-Nets in Base 4

Best Known (222−112, 222, s)-Nets in Base 4

(222−112, 222, 130)-Net over F₄ — Constructive and digital

Digital (110, 222, 130)-net over F₄, using

t-expansion [i] based on digital (105, 222, 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]

(222−112, 222, 165)-Net over F₄ — Digital

Digital (110, 222, 165)-net over F₄, using

t-expansion [i] based on digital (109, 222, 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]

(222−112, 222, 1717)-Net in Base 4 — Upper bound on s

There is no (110, 222, 1718)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46 436220 493700 428021 342018 742616 167512 427480 285995 441639 221449 143090 569678 050599 284664 364854 016465 256520 692469 011550 350990 740731 639600 > 4²²² [i]