MinT - Best Known (231−152, 231, s)-Nets in Base 4

Best Known (231−152, 231, s)-Nets in Base 4

(231−152, 231, 104)-Net over F₄ — Constructive and digital

Digital (79, 231, 104)-net over F₄, using

t-expansion [i] based on digital (73, 231, 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]

(231−152, 231, 112)-Net over F₄ — Digital

Digital (79, 231, 112)-net over F₄, using

t-expansion [i] based on digital (73, 231, 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]

(231−152, 231, 595)-Net in Base 4 — Upper bound on s

There is no (79, 231, 596)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 679358 299745 891253 983568 549543 547770 895502 560654 393699 253370 440651 909490 037325 621174 104584 075619 327083 111873 086325 347409 623707 349653 617508 > 4²³¹ [i]