MinT - Best Known (260−126, 260, s)-Nets in Base 4

Best Known (260−126, 260, s)-Nets in Base 4

(260−126, 260, 130)-Net over F₄ — Constructive and digital

Digital (134, 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]

(260−126, 260, 200)-Net over F₄ — Digital

Digital (134, 260, 200)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−126, 260, 2421)-Net in Base 4 — Upper bound on s

There is no (134, 260, 2422)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 475479 206868 261892 821089 047440 452919 778740 011506 538100 598418 582332 377133 700520 160483 669503 619768 705592 657319 338846 499516 524775 529462 714096 608744 292340 888800 > 4²⁶⁰ [i]