MinT - Best Known (158, 158+46, s)-Nets in Base 4

Best Known (158, 158+46, s)-Nets in Base 4

(158, 158+46, 1048)-Net over F₄ — Constructive and digital

Digital (158, 204, 1048)-net over F₄, using

trace code for nets [i] based on digital (5, 51, 262)-net over F₂₅₆, using
- net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(158, 158+46, 3173)-Net over F₄ — Digital

Digital (158, 204, 3173)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+46, 687596)-Net in Base 4 — Upper bound on s

There is no (158, 204, 687597)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 661 069284 515949 217629 868932 034121 859301 197736 274753 525160 057426 639682 326928 501202 601441 348204 476918 896234 453008 173616 265648 > 4²⁰⁴ [i]