MinT - Best Known (217−141, 217, s)-Nets in Base 4

Best Known (217−141, 217, s)-Nets in Base 4

(217−141, 217, 104)-Net over F₄ — Constructive and digital

Digital (76, 217, 104)-net over F₄, using

t-expansion [i] based on digital (73, 217, 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]

(217−141, 217, 112)-Net over F₄ — Digital

Digital (76, 217, 112)-net over F₄, using

t-expansion [i] based on digital (73, 217, 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]

(217−141, 217, 590)-Net in Base 4 — Upper bound on s

There is no (76, 217, 591)-net in base 4, because

1 times m-reduction [i] would yield (76, 216, 591)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12048 666593 267356 448009 698523 505454 566989 875831 009034 587006 313030 247663 582593 357180 901512 357270 141014 895044 011148 470560 832092 608435 > 4²¹⁶ [i]