MinT - Best Known (260−142, 260, s)-Nets in Base 4

Best Known (260−142, 260, s)-Nets in Base 4

(260−142, 260, 130)-Net over F₄ — Constructive and digital

Digital (118, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(260−142, 260, 168)-Net over F₄ — Digital

Digital (118, 260, 168)-net over F₄, using

t-expansion [i] based on digital (115, 260, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(260−142, 260, 1398)-Net in Base 4 — Upper bound on s

There is no (118, 260, 1399)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 523654 678174 014392 734459 626105 048979 190406 026604 599463 372597 972206 928681 563125 860533 988584 799112 916343 128292 430880 048880 799092 654944 186439 717444 364921 933348 > 4²⁶⁰ [i]