MinT - Best Known (162, 162+54, s)-Nets in Base 4

Best Known (162, 162+54, s)-Nets in Base 4

(162, 162+54, 1028)-Net over F₄ — Constructive and digital

Digital (162, 216, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 54, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(162, 162+54, 1978)-Net over F₄ — Digital

Digital (162, 216, 1978)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+54, 238630)-Net in Base 4 — Upper bound on s

There is no (162, 216, 238631)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11091 679085 147133 642716 559512 168096 658194 689721 518406 077923 776364 395463 901740 789065 836684 118814 403474 844549 269153 705470 783213 118624 > 4²¹⁶ [i]