MinT - Best Known (260−120, 260, s)-Nets in Base 4

Best Known (260−120, 260, s)-Nets in Base 4

(260−120, 260, 130)-Net over F₄ — Constructive and digital

Digital (140, 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]

(260−120, 260, 234)-Net over F₄ — Digital

Digital (140, 260, 234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−120, 260, 3092)-Net in Base 4 — Upper bound on s

There is no (140, 260, 3093)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 476696 603104 399893 823521 598878 274211 031133 597188 340606 040907 481770 230129 854198 560941 950756 472120 668487 608856 205337 079871 827139 851507 305842 790002 650348 433280 > 4²⁶⁰ [i]