MinT - Best Known (260−140, 260, s)-Nets in Base 4

Best Known (260−140, 260, s)-Nets in Base 4

(260−140, 260, 130)-Net over F₄ — Constructive and digital

Digital (120, 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]

(260−140, 260, 168)-Net over F₄ — Digital

Digital (120, 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]

(260−140, 260, 1487)-Net in Base 4 — Upper bound on s

There is no (120, 260, 1488)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 511780 608205 833739 846102 073658 421236 513942 970248 359408 708991 289474 780819 866200 180867 963240 441449 239095 975721 684832 218027 998944 401728 935915 258127 519657 557591 > 4²⁶⁰ [i]