MinT - Best Known (80, 80+175, s)-Nets in Base 4

Best Known (80, 80+175, s)-Nets in Base 4

(80, 80+175, 104)-Net over F₄ — Constructive and digital

Digital (80, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 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]

(80, 80+175, 112)-Net over F₄ — Digital

Digital (80, 255, 112)-net over F₄, using

t-expansion [i] based on digital (73, 255, 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]

(80, 80+175, 564)-Net in Base 4 — Upper bound on s

There is no (80, 255, 565)-net in base 4, because

1 times m-reduction [i] would yield (80, 254, 565)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 935 117363 715271 480727 079991 083891 905834 636366 047184 813700 689468 714401 628309 468841 837355 635344 468683 526226 017243 786126 559431 050743 811884 249249 976668 947200 > 4²⁵⁴ [i]