MinT - Best Known (260−180, 260, s)-Nets in Base 4

Best Known (260−180, 260, s)-Nets in Base 4

(260−180, 260, 104)-Net over F₄ — Constructive and digital

Digital (80, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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]

(260−180, 260, 112)-Net over F₄ — Digital

Digital (80, 260, 112)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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]

(260−180, 260, 555)-Net in Base 4 — Upper bound on s

There is no (80, 260, 556)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 493006 726689 176731 735346 837716 990196 936029 112305 795885 754129 676525 722508 983163 353844 924201 201273 768362 625875 470643 401796 752912 013627 011857 653818 044092 343760 > 4²⁶⁰ [i]