MinT - Best Known (77, 77+182, s)-Nets in Base 4

Best Known (77, 77+182, s)-Nets in Base 4

(77, 77+182, 104)-Net over F₄ — Constructive and digital

Digital (77, 259, 104)-net over F₄, using

t-expansion [i] based on digital (73, 259, 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]

(77, 77+182, 112)-Net over F₄ — Digital

Digital (77, 259, 112)-net over F₄, using

t-expansion [i] based on digital (73, 259, 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]

(77, 77+182, 525)-Net in Base 4 — Upper bound on s

There is no (77, 259, 526)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 917733 427551 703219 020495 051469 402282 582829 112546 978305 714697 690811 300694 395259 098675 329813 642317 559263 957118 889298 996846 044502 169758 116033 425397 169806 896448 > 4²⁵⁹ [i]