MinT - Best Known (242−164, 242, s)-Nets in Base 4

Best Known (242−164, 242, s)-Nets in Base 4

(242−164, 242, 104)-Net over F₄ — Constructive and digital

Digital (78, 242, 104)-net over F₄, using

t-expansion [i] based on digital (73, 242, 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]

(242−164, 242, 112)-Net over F₄ — Digital

Digital (78, 242, 112)-net over F₄, using

t-expansion [i] based on digital (73, 242, 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]

(242−164, 242, 559)-Net in Base 4 — Upper bound on s

There is no (78, 242, 560)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 375448 399418 952027 220548 089757 435030 538125 495227 252578 963148 845880 240736 541649 618605 160347 402108 449837 035695 657309 011324 435481 937727 644562 390960 > 4²⁴² [i]