MinT - Best Known (240−118, 240, s)-Nets in Base 4

Best Known (240−118, 240, s)-Nets in Base 4

(240−118, 240, 130)-Net over F₄ — Constructive and digital

Digital (122, 240, 130)-net over F₄, using

t-expansion [i] based on digital (105, 240, 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]

(240−118, 240, 178)-Net over F₄ — Digital

Digital (122, 240, 178)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−118, 240, 2091)-Net in Base 4 — Upper bound on s

There is no (122, 240, 2092)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 202737 657501 324097 774818 395305 619693 100129 536628 997805 910227 954229 127821 805738 118449 209838 195684 412302 129902 448601 068730 570305 200996 828335 747200 > 4²⁴⁰ [i]