MinT - Best Known (178, 178+58, s)-Nets in Base 4

Best Known (178, 178+58, s)-Nets in Base 4

(178, 178+58, 1032)-Net over F₄ — Constructive and digital

Digital (178, 236, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 59, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(178, 178+58, 2317)-Net over F₄ — Digital

Digital (178, 236, 2317)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178, 178+58, 308666)-Net in Base 4 — Upper bound on s

There is no (178, 236, 308667)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12194 359664 852213 177924 967390 357060 639642 889917 876485 506593 914227 099210 102749 096721 709665 414781 241202 667676 959224 438088 032606 416576 330798 253168 > 4²³⁶ [i]