MinT - Best Known (79, 229, s)-Nets in Base 4

Best Known (79, 229, s)-Nets in Base 4

(79, 229, 104)-Net over F₄ — Constructive and digital

Digital (79, 229, 104)-net over F₄, using

t-expansion [i] based on digital (73, 229, 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]

(79, 229, 112)-Net over F₄ — Digital

Digital (79, 229, 112)-net over F₄, using

t-expansion [i] based on digital (73, 229, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(79, 229, 600)-Net in Base 4 — Upper bound on s

There is no (79, 229, 601)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 792303 596086 441357 005758 061405 347259 033919 594740 100907 408407 473358 563612 815716 563375 654499 944647 462590 803520 945611 114959 623039 329175 891216 > 4²²⁹ [i]