MinT - Best Known (76, 242, s)-Nets in Base 4

Best Known (76, 242, s)-Nets in Base 4

(76, 242, 104)-Net over F₄ — Constructive and digital

Digital (76, 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]

(76, 242, 112)-Net over F₄ — Digital

Digital (76, 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]

(76, 242, 535)-Net in Base 4 — Upper bound on s

There is no (76, 242, 536)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 380214 025078 369833 419035 870872 339229 364935 961126 247061 898722 736654 482802 388197 347215 932076 667824 427481 261458 364744 514908 522692 125483 355166 005400 > 4²⁴² [i]